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A093069 a(n) = (2^n + 1)^2 - 2. 7
7, 23, 79, 287, 1087, 4223, 16639, 66047, 263167, 1050623, 4198399, 16785407, 67125247, 268468223, 1073807359, 4295098367, 17180131327, 68720001023, 274878955519, 1099513724927, 4398050705407, 17592194433023, 70368760954879, 281475010265087, 1125899973951487 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Cletus Emmanuel calls these "Kynea numbers".

Difference between the smallest digitally balanced number with 2n+4 binary digits and the largest digitally balanced number with 2n+2 binary digits (see A031443): 7 = 9-2 = 1001-10, 23 = 35-12 = 100011-1100, 79 = 135-56 = 10000111-111000 etc. - Juri-Stepan Gerasimov, Jun 01 2011

LINKS

Table of n, a(n) for n=1..25.

Eric Weisstein's World of Mathematics, Near-Square Prime

Index entries for linear recurrences with constant coefficients, signature (7,-14,8).

FORMULA

a(n) = 4^n+2^(n+1)-1.

G.f.: -x*(7-26*x+16*x^2) / ( (x-1)*(2*x-1)*(4*x-1) ). - R. J. Mathar, Jun 01 2011

a(n) = A092431(n+2) - A020522(n+1). - R. J. Mathar, Jun 01 2011

EXAMPLE

G.f. = 7*x + 23*x^2 + 79*x^3 + 287*x^4 + 1087*x^5 + 4223*x^6 + 16639*x^7 + ...

MAPLE

A093069:=n->(2^n+1)^2-2: seq(A093069(n), n=1..30);

MATHEMATICA

a[ n_] := If[ n < 1, 0, 4^n + 2^(n + 1) - 1]; (* Michael Somos, Jul 08 2014 *)

CoefficientList[Series[(7 - 26*x + 16*x^2)/((1 - x)*(2*x - 1)*(4*x - 1)), {x, 0, 30}], x] (* Wesley Ivan Hurt, Jul 08 2014 *)

PROG

(PARI) vector(100, n, (2^n+1)^2-2) \\ Colin Barker, Jul 08 2014

(PARI) Vec(-(16*x^2-26*x+7)/((x-1)*(2*x-1)*(4*x-1)) + O(x^100)) \\ Colin Barker, Jul 08 2014

(MAGMA) [(2^n+1)^2-2 : n in [1..30]]; // Wesley Ivan Hurt, Jul 08 2014

CROSSREFS

Cf. A091514 (primes of the form (2^n + 1)^2 - 2).

Cf. A244663.

Sequence in context: A018886 A145842 A086908 * A003540 A063793 A217233

Adjacent sequences:  A093066 A093067 A093068 * A093070 A093071 A093072

KEYWORD

nonn,easy

AUTHOR

Eric W. Weisstein, Mar 17 2004

EXTENSIONS

More terms from Colin Barker, Jul 08 2014

STATUS

approved

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Last modified December 6 15:11 EST 2016. Contains 278781 sequences.